Magnetic resonance imaging is already extensively known in the prior art. Spins of a target region that is to be imaged are aligned by way of a maximally homogeneous basic magnetic field (B0 field) and excited by way of a radiofrequency excitation, the corresponding magnetic resonance signal that is to be measured describing the decay of the excitation. The field of the radiofrequency excitation is often referred to as the B1 field. A plurality of decay constants are known in this context, in particular T1, T2 and T2*. A spatial resolution is achieved in most cases through the use of gradient fields.
Magnetic resonance imaging is an inherently slow imaging technology which often requires long measurement times. It does, however, offer a great number of image contrasts and has proven itself to be an excellent method for achieving soft part contrasts. The usual contrast that is visible in conventional magnetic resonance images is the result of a combination of different physical parameters of a tissue of a patient that is to be scanned. This mix of factors, in combination with the acquisition technique applied and the acquisition parameters used, determines the contrast obtained.
An approach for obtaining contrast information of biological tissue via magnetic resonance imaging which departs from these “classical” magnetic resonance images is the direct measurement of one or more of the underlying physical properties which are part of the mix that determines the image contrast in the conventional magnetic resonance image. These techniques are commonly referred to as “parametric mapping” and accordingly deliver parameter maps, for example T1 maps, T2 maps or T2* maps. When approaches of the type are used, the resulting image contrast is more independent of the hardware used, the acquisition technique employed and the specific image acquisition parameters used. This advantageously results in a simplification in terms of comparability and consequently clinical diagnosis. Thus, for example, a database of comparative parameter values can be built up, with which values a new parameter dataset, i.e. a new parameter map, can be compared. This means, in other words, that a transition is made from the relative contrast information, which is dependent on many factors, to a single, absolute measure of one or more physical properties.
Techniques for determining parameter maps have been known for a long time already and generally necessitate extremely time-consuming measurements which in the past have severely constrained the clinical benefits. In this regard, methods have recently been proposed in order to accelerate the measurement process by way of an undersampling of the k-space. The undersampling is compensated for by prior knowledge about the measured magnetic resonance signal, wherein, for example, a signal model can be used for the magnetic resonance signal describing the magnetization. It is then possible to determine the parameter map in an iterative optimization method. The class to which these methods belong is usually referred to as model-based approaches.
The magnetic resonance data is typically acquired in the k-space, i.e. in the Fourier domain. It can be demonstrated mathematically that a specific volume of data must be sampled in order to reconstruct a magnetic resonance image free of aliasing artifacts. This correlation is also referred to as the Nyquist sampling theorem. It is nonetheless conceivable that parts of the sampled k-space data are redundant or that prior knowledge is present which can be used in order to synthesize parts of the k-space data, such that there is by all means the possibility to sample less data in the k-space than is demanded by the Nyquist theorem. In a typical acquisition scan, the measurement time scales with the volume of sampled data, so by way of undersampling it is possible to achieve a reduction in the measurement time.
However, data sampling in the sub-Nyquist regime demands new reconstruction techniques that go beyond the immediate Fourier transformation and require prior knowledge about redundancies in the data or the anticipated behavior thereof in order to determine the non-sampled part of the magnetic resonance data. In the context of the exploitation of data redundancies, parallel imaging is a way to achieve an acceleration of an acquisition process. In parallel imaging, a plurality of receive coils are used in parallel during the imaging process. This means that magnetic resonance signals are picked up by a plurality of coils, with the result that redundancy is present. A well-known example of a parallel imaging algorithm is the “generalized autocalibrating partial parallel acquisition”, GRAPPA for short, cf. in this regard, for example, the fundamental article by Mark A. Griswold et al. titled “Generalized autocalibrating partial parallel acquisitions (GRAPPA)”, Magnetic Resonance in Medicine 47 (2002) 6, 1202-1210.
In the context of the determination of parameter maps, the already mentioned model-based approaches have primarily become known, an example hereof being the “model-based accelerated relaxometry by iterative non-linear inversion” technique, MARTINI for short, which is to be described; cf. in this regard also the article by Tilman J. Sumpf et al. titled “Model-based nonlinear inverse reconstruction for T2 mapping using highly undersampled spin-echo MRI”, Journal of Magnetic Resonance Imaging 34 (2011) 2, pages 420-428.
In model-based approaches of this type, therefore, undersampled magnetic resonance data is acquired in the k-space. The signal model (model for the magnetization) now permits hypothesis data serving as comparative data to be determined from a hypothesis for the parameter map. A deviation can be determined by comparing the hypothesis data with the magnetic resonance data. The hypothesis is now iteratively adapted in the optimization method as a function of the deviation or the ultimately obtained best hypothesis is output as the result for the parameter map if an abort condition has been met.
This shall be explained in greater detail hereinbelow briefly for the MARTINI reconstruction technique.
As has already been described, the contrast obtained in a magnetic resonance image acquisition is determined by different physical parameters of the scanned tissue in the target region, just as well as by the acquisition technique and the image acquisition parameters. If it is now assumed that all of these factors are known, the magnetic resonance signal (i.e. the magnetization) can be predicted, with the result that a signal model can be determined for the image acquisition process. An example of such a signal model for a multi-echo spin-echo magnetic resonance sequence is the monoexponential signal decay, which is defined as:M({right arrow over (r)})=ρ({right arrow over (r)})e−TE/T2({right arrow over (r)}),where M is the magnetization at the spatial position {right arrow over (r)} as a function of two tissue parameters, specifically the proton density ρ and the transverse relaxation time T2. The magnetization M is additionally dependent on the predefined image acquisition parameter, echo time TE. As parameters for the parameter map, the tissue parameters ρ and T2 are usually the variables that are to be measured.
It is clear from this example how a model can be used in order to determine the tissue parameters as a parameter map, in this case the proton density ρ and the transverse relaxation time T2. If it is assumed that the resulting magnetic resonance signal M is sampled at a sufficiently large number of echo times TE, the hypotheses for the tissue parameters can be determined by way of a simple curve fitting algorithm. This process is generally performed in an iterative manner. The example also reveals in which way the signal model contains prior knowledge: If the signal model is used as a cost function in an iterative optimization process, the described signal behavior can be imposed on the undersampled magnetic resonance data, as a result of which the desired parameters are effectively estimated in the signal model. MARTINI exploits this prior knowledge by undersampling the k-space in a specific manner on the one hand, and on the other hand using the underlying signal model in order to formulate an inverse problem for a nonlinear iterative reconstruction.
In this case, given knowledge of the iterative reconstruction scheme used, the manner in which the k-space is undersampled can be optimized. The MARTINI reconstruction technique uses a block sampling scheme, which means that the k-space is sampled one block at a time, i.e. in contiguous blocks, the position of the block being changed for each echo time TE. It is therefore conceivable, for example, to deconstruct the k-space in the phase encoding direction into a plurality of equal-sized portions which are repeatedly sampled in succession for different echo times.
Once all the undersampled magnetic resonance data has been acquired, an iterative reconstruction is performed, as already mentioned, in which a rough estimation of the parameter maps is assumed as a hypothesis. The parameter maps are continuously improved in each iteration step using an optimizer which utilizes the prior information, in actuality the measured undersampled magnetic resonance data and the above-described hypothesis data determined from the signal model with the aid of the hypothesis. After a specific number of iterations, either a threshold for the permitted iteration steps is exceeded or the deviation with respect to the magnetic resonance data falls below a predefined maximum permitted threshold value.
In spite of the model-based approaches which permit an undersampling of the k-space in order to determine parameter maps, the measurement times for the parameter maps are still quite long, thus making an improvement desirable in this regard. An additional factor is that determining parameter maps by way of the MARTINI reconstruction technique is susceptible to errors originating from violations of the signal model, i.e. parts of the magnetic resonance data in which the signal model is not suitable for approximating the measured magnetic resonance data. Magnetic resonance data acquired in vivo has various sources of violations of the signal model, these being caused by the blood flow, partial volume effects, head motion, noise and other effects. For this reason an improvement of the model-based approaches is also desirable in this regard.